A river flows westward at 8 m/s. A person wants to go directly across
the river so that the resultant velocity is 12 m/s northward. Find
the velocity of the motorboat that would be required to achieve this
resultant velocity.

A manufacturer of a lightweight mountain tent makes a standard model and
an expedition model. I know the labor hours needed for each by the
cutting and assembly departments, the maximum labor hours available per
week in each department, the distributor, will not take more than 12
expedition tents per week. If the company makes a profit of $50 on each
standard tent and $80 on each expedition tent, how many tents of each
type should be manufactured each week to maximize the weekly profit?